Resonances of a Potential Well with a Thick Barrier

• Autores: D. C. Dobson, F. Santosa, Stephen P. Shipman, Michael I. Weinstein
• Localización: Siam journal on applied mathematics, ISSN 0036-1399, Vol. 73, Nº 4, 2013, págs. 1489-1512
• Idioma: inglés
• DOI: 10.1137/120883694
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• Resumen

  • This work is motivated by the desire to develop a method that allows for easy and accurate calculation of complex resonances of a one-dimensional Schrödinger's equation whose potential is a low-energy well surrounded by a thick barrier. The resonance is calculated as a perturbation of the bound state associated with a barrier of infinite thickness. We show that the corrector to the bound-state energy is exponentially small in the barrier thickness. A simple computational strategy that exploits this smallness is devised and numerically verified to be very accurate. We also provide a study of high-frequency resonances and show how they can be approximated. Numerical examples are given to illustrate the main ideas in this work